Question

McCarver Inc. is considering the following mutually exclusive projects:

	Project A	Project B
Year	Cash Flow	Cash Flow
0	-$5,000	-$5,000
1	200	3,000
2	800	3,000
3	3,000	800
4	5,000	200

At what cost of capital will the net present value of the two projects be the same? (That is, what is the "crossover" rate?) (3 points)

Answer 1

"crossover" rate can be calculated as the IRR of Incremental Cashflow

IRR can be calculated by trail and error method

lets take NPV @16%

Year	Cashflow A	Cashflow B	Incremental Cashflow	PVF@16%	Incremental Cashflow*PVF
0	(5,000)	(5,000)	-	1	0.00
1	200	3,000	(2,800)	0.8621	-2413.79
2	800	3,000	(2,200)	0.7432	-1634.96
3	3,000	800	2,200	0.6407	1409.45
4	5,000	200	4,800	0.5523	2651.00

NPV = PV of inflows - PV of outflows

= 1409.45+2651-2413.79-1634.96

= 11.69

Since NPV is +ve, take a higher rate of 17%

Year	Cashflow A	Cashflow B	Incremental Cashflow	PVF@17%	Incremental Cashflow*PVF
0	(5,000)	(5,000)	-	1	0.00
1	200	3,000	(2,800)	0.8547	-2393.16
2	800	3,000	(2,200)	0.7305	-1607.13
3	3,000	800	2,200	0.6244	1373.62
4	5,000	200	4,800	0.5337	2561.52

NPV = PV of inflows - PV of outflows

= 1373.62+2561.52-2393.16-1607.13

= -65.16

IRR = Crossover rate = R1+((NPV at R1*(R2-R1))/(NPV at R1-Npv at R2))

= 16+((11.69*(17-16))/(11.69+65.16))

= 16+(11.69/76.85)

= 16+0.15211450878

= 16.15%